// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_TRANSLATION_H
#define EIGEN_TRANSLATION_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class Translation
 *
 * \brief Represents a translation transformation
 *
 * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
 * \tparam _Dim the  dimension of the space, can be a compile time value or Dynamic
 *
 * \note This class is not aimed to be used to store a translation transformation,
 * but rather to make easier the constructions and updates of Transform objects.
 *
 * \sa class Scaling, class Transform
 */
template<typename _Scalar, int _Dim>
class Translation
{
  public:
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _Dim)
	/** dimension of the space */
	enum
	{
		Dim = _Dim
	};
	/** the scalar type of the coefficients */
	typedef _Scalar Scalar;
	/** corresponding vector type */
	typedef Matrix<Scalar, Dim, 1> VectorType;
	/** corresponding linear transformation matrix type */
	typedef Matrix<Scalar, Dim, Dim> LinearMatrixType;
	/** corresponding affine transformation type */
	typedef Transform<Scalar, Dim, Affine> AffineTransformType;
	/** corresponding isometric transformation type */
	typedef Transform<Scalar, Dim, Isometry> IsometryTransformType;

  protected:
	VectorType m_coeffs;

  public:
	/** Default constructor without initialization. */
	EIGEN_DEVICE_FUNC Translation() {}
	/**  */
	EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)
	{
		eigen_assert(Dim == 2);
		m_coeffs.x() = sx;
		m_coeffs.y() = sy;
	}
	/**  */
	EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
	{
		eigen_assert(Dim == 3);
		m_coeffs.x() = sx;
		m_coeffs.y() = sy;
		m_coeffs.z() = sz;
	}
	/** Constructs and initialize the translation transformation from a vector of translation coefficients */
	EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector)
		: m_coeffs(vector)
	{
	}

	/** \brief Returns the x-translation by value. **/
	EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }
	/** \brief Returns the y-translation by value. **/
	EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }
	/** \brief Returns the z-translation by value. **/
	EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }

	/** \brief Returns the x-translation as a reference. **/
	EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }
	/** \brief Returns the y-translation as a reference. **/
	EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }
	/** \brief Returns the z-translation as a reference. **/
	EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }

	EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }
	EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }

	EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }
	EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }

	/** Concatenates two translation */
	EIGEN_DEVICE_FUNC inline Translation operator*(const Translation& other) const
	{
		return Translation(m_coeffs + other.m_coeffs);
	}

	/** Concatenates a translation and a uniform scaling */
	EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const UniformScaling<Scalar>& other) const;

	/** Concatenates a translation and a linear transformation */
	template<typename OtherDerived>
	EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear) const;

	/** Concatenates a translation and a rotation */
	template<typename Derived>
	EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived, Dim>& r) const
	{
		return *this * IsometryTransformType(r);
	}

	/** \returns the concatenation of a linear transformation \a l with the translation \a t */
	// its a nightmare to define a templated friend function outside its declaration
	template<typename OtherDerived>
	friend EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear,
																  const Translation& t)
	{
		AffineTransformType res;
		res.matrix().setZero();
		res.linear() = linear.derived();
		res.translation() = linear.derived() * t.m_coeffs;
		res.matrix().row(Dim).setZero();
		res(Dim, Dim) = Scalar(1);
		return res;
	}

	/** Concatenates a translation and a transformation */
	template<int Mode, int Options>
	EIGEN_DEVICE_FUNC inline Transform<Scalar, Dim, Mode> operator*(
		const Transform<Scalar, Dim, Mode, Options>& t) const
	{
		Transform<Scalar, Dim, Mode> res = t;
		res.pretranslate(m_coeffs);
		return res;
	}

	/** Applies translation to vector */
	template<typename Derived>
	inline typename internal::enable_if<Derived::IsVectorAtCompileTime, VectorType>::type operator*(
		const MatrixBase<Derived>& vec) const
	{
		return m_coeffs + vec.derived();
	}

	/** \returns the inverse translation (opposite) */
	Translation inverse() const { return Translation(-m_coeffs); }

	static const Translation Identity() { return Translation(VectorType::Zero()); }

	/** \returns \c *this with scalar type casted to \a NewScalarType
	 *
	 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
	 * then this function smartly returns a const reference to \c *this.
	 */
	template<typename NewScalarType>
	EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Translation, Translation<NewScalarType, Dim>>::type
	cast() const
	{
		return typename internal::cast_return_type<Translation, Translation<NewScalarType, Dim>>::type(*this);
	}

	/** Copy constructor with scalar type conversion */
	template<typename OtherScalarType>
	EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType, Dim>& other)
	{
		m_coeffs = other.vector().template cast<Scalar>();
	}

	/** \returns \c true if \c *this is approximately equal to \a other, within the precision
	 * determined by \a prec.
	 *
	 * \sa MatrixBase::isApprox() */
	EIGEN_DEVICE_FUNC bool isApprox(
		const Translation& other,
		const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
	{
		return m_coeffs.isApprox(other.m_coeffs, prec);
	}
};

/** \addtogroup Geometry_Module */
//@{
typedef Translation<float, 2> Translation2f;
typedef Translation<double, 2> Translation2d;
typedef Translation<float, 3> Translation3f;
typedef Translation<double, 3> Translation3d;
//@}

template<typename Scalar, int Dim>
EIGEN_DEVICE_FUNC inline typename Translation<Scalar, Dim>::AffineTransformType
Translation<Scalar, Dim>::operator*(const UniformScaling<Scalar>& other) const
{
	AffineTransformType res;
	res.matrix().setZero();
	res.linear().diagonal().fill(other.factor());
	res.translation() = m_coeffs;
	res(Dim, Dim) = Scalar(1);
	return res;
}

template<typename Scalar, int Dim>
template<typename OtherDerived>
EIGEN_DEVICE_FUNC inline typename Translation<Scalar, Dim>::AffineTransformType
Translation<Scalar, Dim>::operator*(const EigenBase<OtherDerived>& linear) const
{
	AffineTransformType res;
	res.matrix().setZero();
	res.linear() = linear.derived();
	res.translation() = m_coeffs;
	res.matrix().row(Dim).setZero();
	res(Dim, Dim) = Scalar(1);
	return res;
}

} // end namespace Eigen

#endif // EIGEN_TRANSLATION_H
